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Article Evolution of Speciﬁc Heat Capacity with Temperature for Typical Supports Used for Heterogeneous Catalysts

Xiaojia Lu 1,2, Yanjun Wang 1, Lionel Estel 1 , Narendra Kumar 2, Henrik Grénman 2,* and Sébastien Leveneur 1,* 1 Normandie Univ, INSA Rouen, UNIROUEN, LSPC, EA4704, 76000 Rouen, France; [email protected] (X.L.); [email protected] (Y.W.); [email protected] (L.E.) 2 Laboratory of Industrial Chemistry and Reaction Engineering, Johan Gadolin Process Chemistry Centre, Åbo Akademi University, Biskopsgatan 8, FI-20500 Åbo/Turku, Finland; narendra.kumar@abo.ﬁ * Correspondence: henrik.grenman@abo.ﬁ (H.G.); [email protected] (S.L.); Tel.: +33-2329-566-54 (S.L.) Received: 25 June 2020; Accepted: 20 July 2020; Published: 1 August 2020

Abstract: Heterogeneous catalysts are widely used in the chemical industry. Compared with homogeneous catalysts, they can be easily separated from the reaction mixture. To design and optimize an efficient and safe chemical process one needs to calculate the energy balance, implying the need for knowledge of the catalyst’s specific heat capacity. Such values are typically not reported in the literature, especially not the temperature dependence. To fill this gap in knowledge, the specific heat capacities of commonly utilized heterogeneous catalytic supports were measured at different temperatures in a Tian–Calvet calorimeter. The following materials were tested: activated carbon, aluminum oxide, amberlite IR120 (H-form), H-Beta-25, H-Beta-38, H-Y-60, H-ZSM-5-23, H-ZSM-5-280, silicon dioxide, titanium dioxide, and zeolite 13X. Polynomial expressions were successfully fitted to the experimental data.

Keywords: speciﬁc heat capacity; heterogeneous catalytic material; micro-calorimeter C80

1. Introduction Catalysts play a crucial role in the modern chemical industry, and indirectly the development of society. According to statistics, there are around 30,000 different raw materials and chemical intermediates that are synthesized by using catalysts. These materials are not only related to people’s food, clothing, and housing, but also involve modern high-tech fields such as information transmission, network technology, aerospace [1–3], and bioengineering [4,5]. Today, researchers are committed to developing more efficient, selective, less expensive, and greener industrial catalysts in order to upgrade current chemical production technologies. Heterogeneous catalysts are the most widely used catalysts in industrial production, due to their versatile physicochemical properties, high hydrothermal stability, and efficient catalyst recovery/reusability [6,7]. Indeed, heterogeneous catalysis contributes to about 90% of chemical production processes and to more than 20% of all industrial products [8]. There are numerous types of catalytic materials and supports, among which zeolite, mesoporous catalyst, resin catalyst, alumina, and activated-carbon-based catalysts are typically used in industry. Usually, the characteristics of a catalyst, such as specific surface area, particle size, morphology, porosity, and acidity, are determined, as they are crucial parameters for performance and use in industrial applications. However, the effect of the heat capacity of catalysts on large-scale chemical processes has not received much attention in the literature, even though the thermodynamic properties vary significantly between different catalysts

Processes 2020, 8, 911; doi:10.3390/pr8080911 www.mdpi.com/journal/processes Processes 2020, 8, 911 2 of 12 or catalyst supports. Industrial processes can be performed under non-isothermal conditions with different types of catalysts and catalyst loadings, and many processes are performed in continuous reactors with high catalyst loads. Determining the thermal properties of a catalyst is necessary when evaluating the thermal risk of a process performed under non-isothermal conditions, especially when considering larger-scale production. Besides risk assessment, the heat capacity of the catalyst can influence the operation and temperature profile of a reactor significantly. This issue often arises at the start of a process. The heat capacity of a large catalyst bed can have a significant impact on the energy balance. These aspects can be very important for robust modeling and simulation purposes, which are the basis of the reliable design and operation of chemical processes. However, much attention has typically been focused on determining the physical properties of the bulk phase [9–11] in detail, including heat capacity, while very little data are found for heterogeneous catalysts [12,13]. Differential scanning calorimetry (DSC) [14] is a conventional method for measuring a variety of thermodynamic properties. It has been widely applied to the specific heat capacity (Cp) measurement of different materials, such as frying oil [15], alloys [16], phase change materials [17], and solid lead [18]. However, the sensitivity of measuring and calculating specific heat capacity by general DSC is usually very low, resulting in a relative error of 5–10%, mainly due to the weak baseline reproducibility. In addition, poor correction accuracy is obtained by this method. The calibration of general DSC instruments is usually performed by melting the standard metal, and it is greatly affected by the sample morphology, reaction type, and atmosphere. Moreover, sample adaptability is very poor. The sample is always required to maintain good contact with the bottom of the crucible to ensure excellent heat conduction; thus, the Cp test of powders and large heterogeneous samples is greatly restricted. Furthermore, liquid samples are also not applicable, as small crucibles (<100 µL) are usually used, which are difficult to seal. The Setaram C80 3D Calvet Calorimeter is powerful and flexible. Measurement by C80 is similar to DSC, i.e., the energy difference between the measured substance and the reference substance is determined under a programmed-temperature control. However, the Calvet calorimeter possesses a caloric efficiency of up to 94%, whereas that of typical plate DSC is between 20 and 40%. Besides this, the detector adopts a three-dimensional full-clad calorimetric method, and, contrary to the general DSC, it takes into account the heat flow that may occur inside the sample itself during calorimetry. The C80 measurement is independent of the weight, form, and nature of the sample, the type of cell utilized, the manner of contact between sample and sensor, and the nature of the sweeping gas (inert, oxidizing, wet, etc.), providing an excellent precision, even for samples with irregular shapes or uneven heat conduction. Furthermore, the temperature is raised and lowered at a very consistent, slow rate, which makes the Cp measurement more accurate. The C80 calorimeter has found an application in the precise determination of heat capacities of different materials [19–23]. In this work, a micro-calorimeter (C80) was for the first time applied for determining the specific heat capacity of commonly used catalytic materials/supports as a function of temperature. These data contribute to filling an important gap in knowledge in this area. The data can be used to estimate the kinetic constants and reaction enthalpies of chemical processes at both laboratory and industrial scale. Moreover, the heat capacities are important basic data for safety and risk assessment purposes.

2. Materials and Methods

2.1. Calorimetric Reactor Rystem The C80 Tian–Calvet calorimeter (Figure1), manufactured by Setaram instrumentation, has absolute calibration, featuring a three-dimensional transducer with maximum sensitivity. Its measuring temperature range is between ambient (298 K) and 573 K. The apparatus is equipped with twin detectors and twin cells (a measurement cell and a reference cell), which are surrounded by thermocouples. External thermal interferences in the calorimetric system, such as phi-factor [24], are eliminated by a differential coupling of the measurement and reference detectors, allowing for Processes 2020, 8, x 3 of 12 determination of the heat flow for radiation, convection, and conduction in a very precise way. The standard error of the temperature measurement is 0.1 K, and the standard error of enthalpy measurement is 0.1%. The C80 calorimeter has been successfully applied previously in studying different processes, such as hydration, dehydration, denaturation, dissolution, gas adsorption, phase transition, and monomer polymerization. Moreover, the C80 is operated by Setsoft 2000 (Setaram thermal analysis software), and heat measurement can be carried out under an isothermal mode or a temperature-programmed mode, which makes it an ideal device for the measurement of Cp. The current study employed a C80 micro-calorimeter for the measurement of the specific heat capacity of different catalytic materials, in the temperature range 313–453 K. In order to determine the heat flow (energy absorbed by the samples) at different temperatures, a pair of Hastelloy reversing mixing cells was employed. In the C80, the heat flow determined is proportional to the Cp value. Hence, the heat capacity is calculated directly from the heat flow signal. The isothermal baselines before and after each temperature rise need to be long enough for the system to stabilize and reach stationary conditions. The accuracy of the instrument was successfully verified by sodium chloride before the formal test. The samples were dried overnight in an oven at 393 K before the measurement. The measurement cell was filled with a known amount (0.5–3.1 g) of sample, while the reference cell was kept empty, as shown in Figure 1. The calorimeter was sealed, and the heating was started according Processes 2020, 8, 911 3 of 12 to the following temperature program: After reaching the first set point (313 K), the two cells were left to stabilize for 8400 s before increasing the temperature by 2 K at a speed of 0.5 K/min. During determinationthe heating process, of the the heat variation flow forof heat radiation, flow wa convection,s recorded by and the conduction Setsoft 2000 in software. a very precise The system way. Thewas standardthen kept errorat a constant of the temperature temperature measurement for 4200 s, followed is 0.1 K, by and being the heated standard to the error next of enthalpyset point measurement(333 K) at a speed is 0.1%. of 1 K/min, The C80 andcalorimeter then stabilized has for been 8400 successfully s. These steps applied were repeated previously multiple in studying times diwithfferent regular processes, intervals such until asthe hydration, last heat flow dehydration, peak (at 453 denaturation, K) was gained. dissolution, gas adsorption, phaseThe transition, specific heat and capacity monomer meas polymerization.urement was repeated Moreover, three the times C80 for is each operated catalytic by material Setsoft 2000 and (Setaramwas done thermal with the analysis same, software), single sample, and heat giving measurement a maximum can be standard carried outerror under of 1.79%, an isothermal which modedemonstrated or a temperature-programmed excellent repeatability mode,and the which absolute makes accuracy it an ideal of the device C80.for the measurement of Cp.

Figure 1. (a) General view of the C80 micro-calorimeter from Setaram; (b) the heating block showing Figure 1. (a) General view of the C80 micro-calorimeter from Setaram; (b) the heating block showing the geometry for the reference and measurement cells; (c) the Hastelloy reversing mixing cells utilized the geometry for the reference and measurement cells; (c) the Hastelloy reversing mixing cells utilized in the current work and their contents. in the current work and their contents. The current study employed a C80 micro-calorimeter for the measurement of the specific heat In order to evaluate the standard deviation of the heat capacity measurement, Equation (1) was capacity of different catalytic materials, in the temperature range 313–453 K. In order to determine the employed. heat flow (energy absorbed by the samples) at different temperatures, a pair of Hastelloy reversing n mixing cells was employed. In the C80, the heat flow(C determined− C )2 is proportional to the Cp value. Hence, the heat capacity is calculated directly=  fromi=1 thepi heatp flow signal. The isothermal baselines(1) s(C p ) before and after each temperature rise need to be longn − enough1 for the system to stabilize and reach stationary conditions. The accuracy of the instrument was successfully verified by sodium chloride before the formal test. The samples were dried overnight in an oven at 393 K before the measurement. The measurement cell was filled with a known amount (0.5–3.1 g) of sample, while the reference cell was kept empty, as shown in Figure1. The calorimeter was sealed, and the heating was started according to the following temperature program: After reaching the first set point (313 K), the two cells were left to stabilize for 8400 s before increasing the temperature by 2 K at a speed of 0.5 K/min. During the heating process, the variation of heat flow was recorded by the Setsoft 2000 software. The system was then kept at a constant temperature for 4200 s, followed by being heated to the next set point (333 K) at a speed of 1 K/min, and then stabilized for 8400 s. These steps were repeated multiple times with regular intervals until the last heat flow peak (at 453 K) was gained. The specific heat capacity measurement was repeated three times for each catalytic material and was done with the same, single sample, giving a maximum standard error of 1.79%, which demonstrated excellent repeatability and the absolute accuracy of the C80. In order to evaluate the standard deviation of the heat capacity measurement, Equation (1) was employed. s Pn 2 i= (Cpi Cp) s(C ) = 1 − (1) p n 1 − Processes 2020, 8, x 4 of 12 Processes 2020, 8, 911 4 of 12 where Cpi is the experimental value of the specific heat capacity of the ith measurement, 𝐶 is the arithmetic mean value of the specific heat capacity of the n experimental results considered, and n is where Cpi is the experimental value of the specific heat capacity of the ith measurement, Cp is the thearithmetic number mean of times value the of experiment the specific heatwas capacityrepeatedof for the a catalytic n experimental material results at each considered, temperature, and nwhich is the wasnumber 3 in ofthe times current the work. experiment was repeated for a catalytic material at each temperature, which was 3 in theFigure current 2 shows work. an example of the evolution of heat flow and temperature at a set point (333 K) in a seriesFigure measurement,2 shows an example where ofthe the heat evolution flow cu ofrves heat represent flow and the temperature difference in at heat a set flow point between (333 K) thein a measurement series measurement, cell and the where reference the heat cell flow in the curves presence represent and absence the diff oference the sample. in heat The flow difference between betweenthe measurement the enthalpies cell and of the referencetwo cells, celli.e., in the the energy presence absorbed and absence by the ofsample, the sample. was determined The difference by directlybetween integrating the enthalpies the heat of the flow two peak cells, of i.e., the the samp energyle (blue). absorbed The data by the were sample, corrected was determinedby subtracting by thedirectly corresponding integrating blank the heat (red) flow curve. peak The of the corrected sample (blue).data were The subsequently data were corrected used to by calculate subtracting the theCp valuecorresponding of the sample, blank using (red) curve.Equation The (2). corrected data were subsequently used to calculate the Cp value of the sample, using Equation (2). − = Qc Qb C p Qc Qb (2) Cp = ×−Δ (2) m ∆T × inin which which Qcc andand QQbb areare the the total total heat heat absorbed absorbed in in the the presence presence and and absence absence of of a a sample, sample, respectively, respectively, m is the mass of the sample placed into the measurement cell, and Δ∆T isis the the temperature temperature difference difference before and after heat capacity measurement measurement at at a a certain certain set set point, point, which which was was around around 2 2 K. A similar approach was used in previous articlesarticles published by our group [[25,26].25,26].

C Figure 2. IllustrationIllustration of Cpp measurement withwiththe the C80 C80 for for a a catalytic catalytic material. material. ,■ heat, heat flow_H-ZSM-5-23; flow_H-ZSM-5- N, heat flow_blank; , temperature_H-ZSM-5-23; , temperature_blank. 23; ▲, heat flow_blank; □, temperature_H-ZSM-5-23;4 △, temperature_blank. 2.2. Materials 2.2. Materials The majority of a catalyst’s heat capacity depends on the support, because it is the main constituent The majority of a catalyst’s heat capacity depends on the support, because it is the main of the catalyst. In this study, 11 materials typically used as supports in catalyst preparation were chosen constituent of the catalyst. In this study, 11 materials typically used as supports in catalyst for the precise quantification of Cp values, as listed in Tables1 and2. All materials were received or preparation were chosen for the precise quantification of Cp values, as listed in Tables 1 and 2. All synthesized with high purities ( 99%), and were used without further purification. materials were received or synt≥hesized with high purities (≥99%), and were used without further purification. The measurements of a series were taken directly and consecutively at regular intervals, and the measurement for each sample was repeated three times in order to evaluate repeatability. Table 1 shows the basic information of the catalytic materials, and Table 2 displays the loading amount and the temperature ranges for the Cp measurement of each material.

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Table 1. Type, Physical Form, Molar Ratio of SiO2/Al2O3, and Manufacturer of Catalytic Materials Studied in This Work.

Physical SiO /Al O Type 2 2 3 Manufacturer Form (mol/mol) Activated carbon activated carbon powder - Chemviron Al2O3 aluminum oxide powder - Acros Organics Amberlite IR120, H-form(53.0–58.0% Ion-exchange resin bead - Acros Organics moisture) H-Beta-25 zeolite powder 25 Zeolyst International H-Beta-38 zeolite powder 38 Zeolyst International H-Y-60 zeolite powder 60 Alfa Aesar H-ZSM-5-23 zeolite powder 23 Zeolyst International H-ZSM-5-280 zeolite powder 280 Zeolyst International SiO2 silicon dioxide powder - Merck TiO2 titanium dioxide pellet - Degussa Zeolite 13X zeolite powder 1.8 Fluka

a b Table 2. Loading (m) of Catalytic Materials and Temperature Range (T) of Cp Measurement for Each Material.

m/g T/K Activated carbon 0.98 313–453 Al2O3 2.00 313–453 Amberlite IR120, H-form 1.95 313–363 H-Beta-25 0.48 313–453 H-Beta-38 1.28 313–453 H-Y-60 0.65 313–453 H-ZSM-5-23 1.09 313–453 H-ZSM-5-280 1.55 313–453 SiO2 1.37 313–453 TiO2 3.09 313–453 Zeolite 13X 1.41 313–453 a Standard error of mass for speciﬁc heat capacity measurement is u(m) = 0.0001 g. b Standard error of temperature for speciﬁc heat capacity measurement is u(T) = 0.1 K.

The measurements of a series were taken directly and consecutively at regular intervals, and the measurement for each sample was repeated three times in order to evaluate repeatability. Table1 shows the basic information of the catalytic materials, and Table2 displays the loading amount and the temperature ranges for the Cp measurement of each material.

3. Results and Discussion

Speciﬁc Heat Capacity Calculation Eleven commonly utilized catalytic materials, ranging from gel-type anion exchange resins to pure alumina, were studied in a wide temperature range (313–453 K), and the results are shown in Table3. The data show excellent repeatability of the measurements, as a relatively low combined 1 1 expanded uncertainty value (U(Cp) = 31.50 J kg K , 0.95 level of conﬁdence) was observed. · − · − Processes 2020, 8, 911 6 of 12

Table 3. Average Values of Speciﬁc Heat Capacity (Cp) of Catalytic Materials as a Function of Temperature (T) a.

b 1 1 1 1 1 1 T/K Cp /(J kg K ) T/K Cp/(J kg K ) T/K Cp/(J kg K ) · − · − · − · − · − · − Activated carbon 313.59 997.75 382.88 1241.17 422.42 1440.42 333.36 1037.55 392.74 1288.34 432.34 1459.99 353.13 1091.18 402.60 1355.75 442.21 1493.63 372.96 1179.32 412.49 1413.87 452.10 1506.95

Al2O3 313.57 857.01 382.84 980.10 422.40 1041.78 333.36 903.54 392.73 1003.09 432.31 1052.30 353.15 940.53 402.62 1015.48 442.22 1070.46 372.93 970.32 412.51 1033.37 452.10 1083.82 Amberlite IR120, H-form 313.60 1170.74 333.40 1244.29 353.21 1325.63 323.50 1208.66 343.31 1285.37 363.09 1361.98 H-Beta-25 313.62 1048.08 382.91 1326.90 422.47 1526.61 333.41 1135.92 392.78 1360.29 432.38 1577.30 353.20 1200.45 402.67 1419.67 442.25 1611.05 373.01 1259.04 412.56 1476.82 452.14 1647.16 H-Beta-38 313.63 1361.17 382.93 1632.81 422.50 1896.06 333.42 1428.30 392.81 1685.38 432.41 1983.12 353.22 1499.17 402.70 1757.74 442.28 2090.75 373.03 1575.57 412.59 1819.02 452.17 2201.44 H-Y-60 313.59 895.66 382.86 1041.12 422.46 1137.74 333.38 935.65 392.75 1061.84 432.34 1160.56 353.18 979.14 402.64 1085.68 442.22 1184.64 372.97 1019.52 412.55 1110.76 452.12 1209.15 H-ZSM-5-23 313.60 1027.35 382.87 1167.70 422.44 1277.33 333.39 1063.39 392.77 1194.68 432.36 1313.73 353.18 1098.71 402.65 1219.61 442.25 1353.51 372.97 1143.54 412.54 1246.26 452.13 1392.11 H-ZSM-5-280 313.62 828.34 382.90 896.44 422.47 944.23 333.41 864.92 392.79 910.64 432.38 956.91 353.21 865.08 402.68 927.66 442.26 975.72 373.00 882.80 412.58 940.17 452.15 976.01

SiO2 313.59 1045.04 382.85 1333.53 422.43 1629.69 333.38 1112.58 392.75 1399.71 432.34 1727.41 353.15 1163.06 402.65 1465.91 442.21 1836.38 372.95 1277.84 412.54 1560.48 452.10 1939.65

TiO2 313.61 702.41 382.88 773.06 422.45 796.51 333.40 725.88 392.77 780.21 432.35 805.09 353.20 746.42 402.66 788.29 442.24 813.76 372.99 757.83 412.57 793.80 452.13 818.09 Zeolite 13X 313.61 1004.46 382.89 1110.27 422.48 1149.40 333.41 1043.91 392.77 1114.40 432.37 1173.65 353.20 1072.98 402.67 1128.13 442.25 1174.02 373.00 1097.44 412.58 1136.84 452.14 1185.55 a Standard error of temperature for specific heat capacity measurement is u(T) = 0.1 K. b Combined expanded 1 1 uncertainty for specific heat capacity is U(Cp) = 31.50 J kg K (0.95 level of confidence). · − · − Processes 2020, 8, x 7 of 12

333.38 1112.58 392.75 1399.71 432.34 1727.41 353.15 1163.06 402.65 1465.91 442.21 1836.38 372.95 1277.84 412.54 1560.48 452.10 1939.65 TiO2 313.61 702.41 382.88 773.06 422.45 796.51 333.40 725.88 392.77 780.21 432.35 805.09 353.20 746.42 402.66 788.29 442.24 813.76 372.99 757.83 412.57 793.80 452.13 818.09 Zeolite 13X 313.61 1004.46 382.89 1110.27 422.48 1149.40 333.41 1043.91 392.77 1114.40 432.37 1173.65 353.20 1072.98 402.67 1128.13 442.25 1174.02 373.00 1097.44 412.58 1136.84 452.14 1185.55 Processesa Standard2020, 8, 911 error of temperature for specific heat capacity measurement is u(T) = 0.1 K. b Combined7 of 12 expanded uncertainty for specific heat capacity is U(Cp) = 31.50 J·kg−1·K−1 (0.95 level of confidence).

C Figure3 3a,ba,b displaydisplay thethe Cp values of the materials as a function of temperature. It is clear that the heat capacitiescapacities of of di ffdifferenterent catalytic catalytic materials materials at the sameat the temperature same temperature are not similar, are not which similar, significantly which significantlyinfluences operation influences under operation non-isothermal under non-isothermal conditions. conditions.

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◆

Figure 3.3. CCppvalues values of of (a )(a catalytic) catalytic materials materials containing containi aluminang alumina or silica, or andsilica, (b )and other (b catalytic) other materialscatalytic as a function of temperature. , activated carbon; , Al O ; , amberlite IR120, H-form; N, H-Beta-25; materials as a function of temperature. □, activated carbon;2 3 4■, Al2O3; △, amberlite IR120, H-form; ▲, , H-Beta-38;◇◆ , H-Y-60; ◆, H-ZSM-5-23; , H-ZSM-5-280; ☆, SiO2; F, TiO2; , zeolite 13X.▽ H-Beta-25; , H-Beta-38; , H-Y-60; ○, H-ZSM-5-23;• ●, H-ZSM-5-280; ☆, SiO5 2; ★, TiO2; , zeolite 13X.3 # One can observe that the speciﬁc heat capacity of the selected catalytic materials does not have the sameOne behavior can observe as a function that the of specific temperature. heat capacity In general, of the when selected the temperature catalytic materials increases, does the not speciﬁc have ☆ theheat same capacity behavior increases. as a function of temperature. In general, when the temperature increases, the specific heat capacity increases. The specific heat capacities of alumina silicate materials are influenced by both the silica and alumina. There is not a clear relationship between the Cp of these materials and the SiO2/Al2O3 ratio. One can notice that the Cp values of H-Beta-38 and SiO2 are more sensitive to temperature compared with the other materials (Figure 3). The Cp values of TiO2 are almost independent of temperature. The obtained Cp values were compared with previously published data [27], as plotted in Figure 4. The Cp values obtained for both activated carbon and alumina are higher than those reported in the literature, even though the curves of the experimental value and the corresponding reference value seem to be parallel to each other. This may be due to the use of different instruments and their related measurement mechanisms. However, a very significant difference in Cp values was obtained for activated carbon and graphite, which are chemically very similar. This was probably caused by the different crystal morphology of these two materials, but not structurally caused, because activated carbon has high porosity. However, further studies are needed to explore the influence of different factors on the heat capacity of these catalytic materials, such as crystallinity, specific surface area, and pore size distribution. Based on the literature [25,26,28], the evolution of Cp with temperature follows a polynomial dependence of the second order. The experimental data in this study were correlated with Equation (3). The fitting parameters, as well as the coefficient of determination (R2), are given in Table 4. = + × − + × 2 − 2 C p (T ) C p (Tref ) A （T Tref ) B （T Tref ) (3) where T and Tref are the measured temperatures and reference temperature in Kelvin; A and B are constants determined by the inherent properties of the material.

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The specific heat capacities of alumina silicate materials are influenced by both the silica and alumina. There is not a clear relationship between the Cp of these materials and the SiO2/Al2O3 ratio. One can notice that the Cp values of H-Beta-38 and SiO2 are more sensitive to temperature compared with the other materials (Figure3). The Cp values of TiO2 are almost independent of temperature. The obtained Cp values were compared with previously published data [27], as plotted in Figure4. The Cp values obtained for both activated carbon and alumina are higher than those reported in the literature, even though the curves of the experimental value and the corresponding reference value seem to be parallel to each other. This may be due to the use of different instruments and their related measurement mechanisms. However, a very significant difference in Cp values was obtained for activated carbon and graphite, which are chemically very similar. This was probably caused by the different crystal morphology of these two materials, but not structurally caused, because activated carbon has high porosity. However, further studies are needed to explore the influence of different factors on the heat capacity of these catalytic materials, such as crystallinity, specific surface area, Processesand pore 2020 size, 8, x distribution. 9 of 12

Figure 4. Comparison of Cp values between the current work and references. , activated carbon_exp; Figure 4. Comparison of Cp values between the current work and references. ●•, activated carbon_exp; oo,, graphite_ref. graphite_ref. [27]; [27]; ■,, Al Al22OO3_exp;3_exp; □, Al, Al2O2O3_ref.3_ref. [27]. [27 ].

ToBased compare on the the literature fit of the [25 polynomial,26,28], the expression evolution ofwithCp thewith experimental temperature results, follows Athena a polynomial Visual Studiodependence [29] was of the used second to calculate order. The the experimental errors of the data estimated in this studyfittingwere parameters. correlated The with obtained Equation error (3). 2 valuesThe ﬁtting provide parameters, a 0.95 confidence as well as interval. the coeﬃ cient of determination (R ), are given in Table4.

2 2 Cp(T) = Cp(Tre f ) + A (T Tre f ) + B (T Tre f ) (3) Table 4. Correlation Results of Cp Data for× Different− Catalytic× Materials− with Equation (3). where T and Tref are the measured temperatures andEstimated reference temperature inEstimated Kelvin; A and B are Cp(Tref)/(J A/(J·kg−1· Tref/K Error of B/(J·kg−1·K−3) Error of R2 constants determined by the·kg inherent−1·K−1) propertiesK−2) of the material. A/(J·kg−1·K−2) B/(J·kg−1·K−3) Activated 392.74 1288.34 2.89 5.57 0.0016 0.0072 0.9992 carbon Al2O3 392.73 1003.09 4.37 0.79 −0.0036 0.0010 0.9971 Amberlite 353.21 1325.63 3.94 0.09 0.9992 IR120, H-form H-Beta-25 402.67 1419.67 4.42 0.28 0.9910 H-Beta-38 392.81 1685.38 −19.39 2.47 0.0329 0.0032 0.9981 H-Y−60 372.97 1019.52 0.42 0.35 0.0024 0.0004 0.9998 H-ZSM-5-23 392.77 1194.68 -3.87 0.75 0.0084 0.0010 0.9991 H-ZSM-5-280 392.79 910.64 1.08 0.12 0.9729 SiO2 392.75 1399.71 −1.94 1.58 0.0337 0.0021 0.9994 TiO2 402.66 788.29 2.92 0.62 −0.0027 0.0008 0.9944 Zeolite 13X 373.00 1097.44 3.44 1.24 −0.0029 0.0016 0.9907

As can be seen from Table 4, a very satisfactory correlation was obtained for each sample, with a coefficient of determination higher than 97%, although the estimated errors for parameters A and B were not always low. A linear relationship between Cp and T was found for Amberlite IR120, H- Beta-25, and H-ZSM-5-280 in the measured temperature range. Thus, for these materials, the value of B was set to 0.

4. Conclusions

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Table 4. Correlation Results of Cp Data for Diﬀerent Catalytic Materials with Equation (3).

1 1 1 2 Estimated Error 1 3 Estimated Error 2 Tref/K Cp(Tref)/(J kg K ) A/(J kg K ) B/(J kg K ) R · − · − · − · − of A/(J kg 1 K 2) · − · − of B/(J kg 1 K 3) · − · − · − · − Activated carbon 392.74 1288.34 2.89 5.57 0.0016 0.0072 0.9992 Al O 392.73 1003.09 4.37 0.79 0.0036 0.0010 0.9971 2 3 − Amberlite IR120, H-form 353.21 1325.63 3.94 0.09 0.9992 H-Beta-25 402.67 1419.67 4.42 0.28 0.9910 H-Beta-38 392.81 1685.38 19.39 2.47 0.0329 0.0032 0.9981 − H-Y 60 372.97 1019.52 0.42 0.35 0.0024 0.0004 0.9998 − H-ZSM-5-23 392.77 1194.68 -3.87 0.75 0.0084 0.0010 0.9991 H-ZSM-5-280 392.79 910.64 1.08 0.12 0.9729 SiO 392.75 1399.71 1.94 1.58 0.0337 0.0021 0.9994 2 − TiO 402.66 788.29 2.92 0.62 0.0027 0.0008 0.9944 2 − Zeolite 13X 373.00 1097.44 3.44 1.24 0.0029 0.0016 0.9907 − Processes 2020, 8, 911 10 of 12

To compare the fit of the polynomial expression with the experimental results, Athena Visual Studio [29] was used to calculate the errors of the estimated fitting parameters. The obtained error values provide a 0.95 confidence interval. As can be seen from Table4, a very satisfactory correlation was obtained for each sample, with a coefficient of determination higher than 97%, although the estimated errors for parameters A and B were not always low. A linear relationship between Cp and T was found for Amberlite IR120, H-Beta-25, and H-ZSM-5-280 in the measured temperature range. Thus, for these materials, the value of B was set to 0.

4. Conclusions In this study, the evolution of specific heat capacity with temperature was measured for different materials used in the preparation of heterogeneous catalysts. Such a study is important in developing efficient and safe chemical processes. A commercial Tian–Calvet calorimeter was successfully used, allowing for high accuracy and the possibility of working at high temperatures. Different families of catalytic materials were tested, including alumina-silicates, aluminum oxide, silicon dioxide, titanium dioxide, activated carbon, and sulfonated resin. It was found that the specific heat capacities increase, to a varying degree, with temperature for these catalytic materials. For example, the Cp of silicon dioxide was more sensitive to a temperature increase than titanium dioxide. A polynomial correlation for each catalytic material was developed. However, there is not a clear correlation between the Al2O3/SiO2 ratio and the values of Cp. Further investigation is needed to develop stronger relationships, taking into account the effect of catalyst structure and intrinsic properties on the specific heat capacities of these catalytic materials.

Author Contributions: Conceptualization, S.L.; methodology, Y.W.; software, S.L.; validation, X.L.; formal analysis, X.L.; investigation, X.L.; resources, N.K.; writing—original draft preparation, X.L., H.G., and S.L.; writing—review and editing, X.L., H.G., L.E., and S.L.; supervision, H.G., L.E., and S.L. All authors have read and agreed to the published version of the manuscript. Funding: This study has been done in the framework of Task 2: “Green process: 2nd generation of biomass” of the AMED project. The authors thank the AMED project. The AMED project has been funded with support from the European Union, the European Regional Development Fund (ERDF), and the Regional Council of Normandie. The China Scholarship Council: Cooperation Program with the UTs and INSAs (France) is thanked by the authors. The authors thank the Erasmus program. Conﬂicts of Interest: The authors declare no conﬂicts of interest.

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